Legal claims defining the scope of protection, as filed with the USPTO.
1. A computer-implemented method for predicting whether a point on a computer generated surface is adjacent to laminar or turbulent fluid flow, the method comprising: obtaining, using a computer, a plurality of boundary-layer properties at the point on the computer-generated surface using a steady-state solution of a fluid flow in a region adjacent to the point; obtaining, using the computer, a plurality of instability modes, wherein one or more mode parameters define each instability mode; obtaining, using the computer, a vector of regressor weights of known instability growth rates in a training dataset; for each instability mode in the plurality of instability modes: determining, using the computer, a covariance vector comprising a covariance of a predicted local instability growth rate for the point with respect to each of the known instability growth rates in the training dataset; and determining, using the computer, the predicted local instability growth rate at the point for the instability mode using the vector of regressor weights and the covariance vector; and determining, using the computer, an n-factor envelope at the point for the plurality of instability modes using the predicted local instability growth rates, wherein the n-factor envelope is indicative of whether the point is adjacent to laminar or turbulent flow.
2. The method of claim 1 , further comprising: determining whether the fluid flow at the point is turbulent or laminar based on whether the n-factor envelope at the point exceeds a threshold value, wherein if the n-factor envelope at the point exceeds the threshold value, then the point is adjacent to turbulent flow and wherein if the n-factor envelope at the point is less than the threshold value, then the point is adjacent to laminar flow.
3. The method of claim 1 , wherein the training dataset includes a training input vector associated with each known instability growth rate, wherein each training input vector includes training boundary-layer properties and at least one training instability mode parameter, wherein the vector of regressor weights is based on a covariance matrix, wherein the covariance matrix has elements that are covariances of one known instability mode with respect to another known instability mode, wherein a covariance of a first known instability mode with respect to a second known instability mode is based on a distance between a first and a second training input vectors associated with a first and a second known instability growth rates, respectively, wherein the predicted local instability growth rate is associated with the plurality of boundary-layer properties and at least one training instability mode parameter describing an instability mode, wherein the covariance for the predicted local instability growth rate with respect to a known instability growth rate is based on a distance from the plurality of boundary-layer properties and the at least one training instability mode parameter to the training input vector associated with the known instability growth rate.
4. The method of claim 3 , further comprising: determining whether the fluid flow at the point is turbulent or laminar based on whether the n-factor envelope at the point exceeds a threshold value, wherein if the n-factor envelope at the point exceeds the threshold value, then the point is adjacent to turbulent flow and wherein if the n-factor envelope at the point is less than the threshold value, then the point is adjacent to laminar flow.
5. The method of claim 3 , wherein the training dataset is a subset of one partition of a plurality of partitions of a larger dataset, wherein the known instability growth rates are added to the subset from the partition based on a prediction error associated with predicting the local instability growth rate, and wherein the one partition is chosen based on the boundary-layer properties or the at least one training instability mode parameter.
6. The method of claim 3 , wherein the covariance matrix is based on a squared exponential covariance function.
7. The method of claim 3 , wherein the covariance matrix and the covariance vector are based on a squared exponential covariance function.
8. The method of claim 1 , wherein the plurality of instability modes is of a stationary crossflow type, and wherein each of the plurality of instability modes has a temporal frequency of zero.
9. The method of claim 8 , wherein the plurality of boundary-layer properties include crossflow Reynolds number, crossflow velocity ratio, crossflow shape factor, and wall to external temperature ratio, and wherein one mode parameter defining the plurality of instability modes is a spanwise wavelength of the mode.
10. The method of claim 1 , wherein the training dataset is generated with linear stability theory (LST) model analysis.
11. The method of claim 1 , wherein the training dataset is constructed by: obtaining a larger dataset of known instability growth rates; adding a subset of known instability growth rates that are in the larger dataset to the training dataset; determining a prediction error between a known instability growth rate in the larger dataset that is not in the training dataset and the predicted local instability growth rate; and based on the prediction error, adding the known instability growth rate to the training dataset from the larger dataset.
12. The method of claim 1 , wherein the training dataset is one partition of a plurality of partitions of a larger dataset.
13. The method of claim 1 , wherein the training dataset is a subset of one partition of a plurality of partitions of a larger dataset and wherein the known instability growth rates are added to the subset from the partition based on a prediction error associated with predicting the local instability growth rate.
14. The method of claim 1 further comprising: determining a confidence measure for the predicted local instability growth rate, wherein the confidence measure is based on the covariance of the predicted local instability growth rate with respect to the known instability growth rates in the training dataset.
15. The method of claim 14 further comprising: if the confidence measure indicates error above a threshold, adding additional known instability growth rates to the training dataset.
16. The method of claim 1 , wherein the computer-generated surface is a computer-generated aircraft surface.
17. A nontransitory computer-readable medium storing computer-readable instructions which when executed on a computer perform a method for predicting whether a point on a computer-generated surface is adjacent to laminar or turbulent fluid flow, the medium including instructions for: obtaining a plurality of boundary-layer properties at the point on the computer-generated surface using a steady-state solution of a fluid flow in a region adjacent to the point; obtaining a plurality of instability modes, wherein one or more mode parameters define each instability mode; obtaining a vector of regressor weights of known instability growth rates in a training dataset; for each instability mode in the plurality of instability modes: determining a covariance vector comprising a covariance of a predicted local instability growth rate for the point with respect to each of the known instability growth rates in the training dataset; and determining the predicted local instability growth rate at the point for the instability mode using the vector of regressor weights and the covariance vector; and determining an n-factor envelope at the point for the plurality of instability modes using the predicted local instability growth rates, wherein the n-factor envelope is indicative of whether the point is adjacent to laminar or turbulent flow.
18. The computer-readable medium of claim 17 , further comprising instructions for: determining whether the fluid flow at the point is turbulent or laminar based on whether the n-factor envelope at the point exceeds a threshold value, wherein if the n-factor envelope at the point exceeds the threshold value, then the point is adjacent to turbulent flow and wherein if the n-factor envelope at the point is less than the threshold value, then the point is adjacent to laminar flow.
19. The computer-readable medium of claim 17 , wherein the training dataset includes a training input vector associated with each known instability growth rate, wherein each training input vector includes training boundary-layer properties and at least one training instability mode parameter, wherein the vector of regressor weights is based on a covariance matrix, wherein the covariance matrix has elements that are covariances of one known instability mode with respect to another known instability mode, wherein a covariance of a first known instability mode with respect to a second known instability mode is based on a distance between a first and a second training input vectors associated with a first and a second known instability growth rates, respectively, wherein the predicted local instability growth rate is associated with the plurality of boundary-layer properties and at least one training instability mode parameter describing an instability mode, wherein the covariance for the predicted local instability growth rate with respect to a known instability growth rate is based on a distance from the plurality of boundary-layer properties and the at least one training instability mode parameter to the training input vector associated with the known instability growth rate.
20. The computer-readable medium of claim 19 , further comprising instructions for: determining whether the fluid flow at the point is turbulent or laminar based on whether the n-factor envelope at the point exceeds a threshold value, wherein if the n-factor envelope at the point exceeds the threshold value, then the point is adjacent to turbulent flow and wherein if the n-factor envelope at the point is less than the threshold value, then the point is adjacent to laminar flow.
21. The computer-readable medium of claim 19 , wherein the training dataset is a subset of one partition of a plurality of partitions of a larger dataset, wherein the known instability growth rates are added to the subset from the partition based on a prediction error associated with predicting the local instability growth rate, and wherein the one partition is chosen based on the boundary-layer properties or the at least one training instability mode parameter.
22. The computer-readable medium of claim 19 , wherein the covariance matrix is based on a squared exponential covariance function.
23. The computer-readable medium of claim 19 , wherein the covariance matrix and the covariance vector are based on a squared exponential covariance function.
24. The computer-readable medium of claim 17 , wherein the plurality of instability modes is of a stationary crossflow type, and wherein each of the plurality of instability modes has a temporal frequency of zero.
25. The computer-readable medium of claim 24 , wherein the plurality of boundary-layer properties include crossflow Reynolds number, crossflow velocity ratio, crossflow shape factor, and wall to external temperature ratio, and wherein one mode parameter defining the plurality of instability modes is a spanwise wavelength of the mode.
26. The computer-readable medium of claim 17 , wherein the training dataset is generated with linear stability theory (LST) model analysis.
27. The computer-readable medium of claim 17 , wherein the training dataset is constructed by: obtaining a larger dataset of known instability growth rates; adding a subset of known instability growth rates that are in the larger dataset to the training dataset; determining a prediction error between a known instability growth rate in the larger dataset that is not in the training dataset and the predicted local instability growth rate; and based on the prediction error, adding the known instability growth rate to the training dataset from the larger dataset.
28. The computer-readable medium of claim 17 , wherein the dataset is one partition of a plurality of partitions of a larger dataset.
29. The computer-readable medium of claim 17 , wherein the training dataset is a subset of one partition of a plurality of partitions of a larger dataset and wherein the known instability growth rates are added to the subset from the partition based on a prediction error associated with predicting the local instability growth rate.
30. The computer-readable medium of claim 17 further comprising instructions for: determining a confidence measure for the predicted local instability growth rate, wherein the confidence measure is based on the covariance of the predicted local instability growth rate with respect to the known instability growth rates in the training dataset.
31. The computer-readable medium of claim 30 further comprising instructions for: if the confidence measure indicates error above a threshold, adding additionally known instability growth rates to the training dataset.
32. The method of claim 17 , wherein the computer-generated surface is a computer-generated aircraft surface.
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September 17, 2013
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